ACT Math : Parallel Lines

Example Questions

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Example Question #33 : Algebra

What is the slope of any line parallel to the line ?

Explanation:

To answer this question, we must find the slope of a line parallel to the line .

When a line is parallel to another, they have the same slope. Therefore, if we find the slope of the line we are given, we will find the slope of any line that would be parallel to it.

To find the slope, we must put our equation into point-intercept form. Point-intercept form is displayed as the following:

, where  is the slope and  is where the line intercepts the -axis.

Note that to put a line into point-intercept form, you must solve for .

Therefore, we must solve for . So, for this data, we must first subtract both sides of the equation by :

This becomes:

Now we must divide each side by  to get  by itself:

This becomes:

Because  is  in our point-intercept form, the slope of our line is . Therefore, the slope of any line parallel to this line is also .

Example Question #34 : Algebra

What is the slope of a line parallel to the line given by the equation:
?

Explanation:

Parallel lines have the same slope. You find slope by using the general form of slope-intercept:

where  represents the slope of the line and  represents the -intercept.

For our equation we see that the

is

thus the anser is .

Example Question #1 : How To Find The Slope Of Parallel Lines

What is the slope of a line parallel to the line defined by the equation:

Explanation:

The slope of a line in slope-intercept form is given by the coefficient,  in the equation:

. For two lines to be parallel, they have to have the same slope. Thus we see in our equation that  and so a line that is parallel must also have a slope of

Example Question #2 : How To Find The Slope Of Parallel Lines

Which of the following is the equation of a line parallel to the line .

Explanation:

Parallel lines have equivalent slopes, so the correct answer is .

Example Question #5 : How To Find Out If Lines Are Parallel

Which of the following lines is parallel to:

Explanation:

First write the equation in slope intercept form. Add  to both sides to get . Now divide both sides by  to get . The slope of this line is , so any line that also has a slope of  would be parallel to it. The correct answer is  .

Example Question #7 : How To Find Out If Lines Are Parallel

Which pair of linear equations represent parallel lines?

Explanation:

Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "" spot in the linear equation

We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.

Example Question #8 : How To Find Out If Lines Are Parallel

Which of the following equations represents a line that is parallel to the line represented by the equation ?

Explanation:

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Because the given line has the slope of , the line parallel to it must also have the same slope.

Example Question #1 : How To Find Out If Lines Are Parallel

Line  passes through the points  and . Line  passes through the point  and has a  of . Are the two lines parallel? If so, what is their slope? If not, what are their slopes?

Yes, the lines are parallel with a slope of .

Yes, the lines are parallel with a slope of .

No, the lines are not parallel. Line  has a slope of  and line  has a slope of .

No, the lines are not parallel. Line  has a slope of  and line  has slope .

Yes, the lines are parallel with a slope of .

Explanation:

Finding slope for these two lines is as easy as applying the slope formula to the points each line contains. We know that line  contains points  and , so we can apply our slope formula directly (pay attention to negative signs!)

.

Line  contains point  and, since the y-intercept is always on the vertical axis, . Thus:

The two lines have the same slope, , and are thus identical.

Example Question #2 : How To Find Out If Lines Are Parallel

Line  is described by the equation . Line  passes through the points  and . Are the two lines parallel? If so, what is their slope? If not, what are their slopes?

No, the lines are not parallel. Line  has slope  and line  has slope .

Yes, the lines are parallel, and both lines have slope .

Yes, the lines are parallel, and both lines have slope .

No, the lines are not parallel. Line  has slope  and line  has slope .

No, the lines are not parallel. Line  has slope  and line  has slope .

Explanation:

We are told at the beginning of this problem that line  is described by  . Since  is our slope-intecept form, we can see that  for this line. Since parallel lines have equal slopes, we must determine if line  has a slope of .

Since we know that  passes through points  and , we can apply our slope formula:

Thus, the slope of line  is 1. As the two lines do not have equal slopes, the lines are not parallel.

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